Mastering Quadratic Functions: Converting Standard Form To Vertex Form

vertex form of a quadratic function

A quadratic function written in the form f(x)=a(x-h)^2+k, where a is not equal to 0 and where a, h, and k are constants and (h,k) is the vertex.

The vertex form of a quadratic function is written as:

f(x) = a(x – h)^2 + k

Where a is the coefficient of the quadratic term, and h and k are the coordinates of the vertex. The values of a, h, and k can be obtained from the standard form of a quadratic equation:

f(x) = ax^2 + bx + c

To convert a quadratic function in standard form to vertex form, we complete the square as follows:

f(x) = a(x^2 + bx/a) + c

f(x) = a(x^2 + bx/a + (b/2a)^2 – (b/2a)^2) + c

f(x) = a(x + b/2a)^2 – (b/2a)^2 + c

The value of a remains the same in vertex form as in standard form. The vertex is located at the point (-b/2a, -b^2/4a + c).

More Answers:
Why The Sum Of A Rational And Irrational Number Always Results In An Irrational Number – Math Explanation.
Rational Numbers: Addition And Multiplication Explained
Discovering The Vertex Of A Parabola: Formulas And Techniques

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